Tightness diagonal

Identity reactions (defined as reactions giving product identical with the reactant) are very useful for discussions of concerted nucleophilic displacements because they require that the transition structure lies on the tightness diagonal shown in the More O Ferrall-Jencks reaction map... 

Figure The tightness diagonal is sometimes called the disparity... 

The elements on the right side of the chart have more electrons j in their outer shells than those on the left, but their nuclei hold I them more tightly. Only the elements in Groups IV and V that have large atoms permit enough free electron movement for them to behave as metals. A diagonal line drawn down the chart from boron to bismuth divides the metals from the nonmetals. None of the elements above the line are metallic. 

Canonical transformations from the tight-binding (atomic orbitals) representation to the eigenstate (molecular orbitals) representation play an important role, and we consider it in detail. Assume, that we find two unitary matrices SR and SR, such that the Hamiltonians of the left part Hi and of the right part Hi can be diagonalized by the canonical transformations... 

The tight-binding band structure calculations were based upon the effective one-electron Hamiltonian of the extended Huckel method. [5] The off-diagonal matrix elements of the Hamiltonian were calculated acording to the modified Wolfsberg-Helmholtz formula. All valence electrons were explicitly taken into account in the calculations and the basis set consisted of double- Slater-type orbitals for C, O and S and a single- Slater-type orbitals for H. The exponents, contraction coefficients and atomic parameters were taken from previous work [6],... 

For the sake of simplicity, we consider a tight-binding Hamiltonian with one orbital per site, at regular lattice positions r . We consider specifically the case of diagonal disorder, neglecting at this stage off-diagonal and environmental disorder. The simplest model Hamiltonian which embodies the above features is of the type... 

At the lowest level of sophistication of quantum treatments, the tight-binding method and the semi-empirical HF method reduce the complexity of the interacting electron system to the diagonalization of an effective one-electron Hamiltonian matrix, whose elements contain empirical parameters. The electronic wave functions are expanded on a minimal basis set of atomic or Slater orbitals centered on the atoms and usually restricted to valence orbitals. The matrix elements are self-consistently determined or not, depending upon the method. 

Fig. 4 A transition state for phosphoryl transfer in which bond fission is ahead of bond formation to the phosphoryl acceptor (nucleophile) is loose, and resides in the lower right region. In the reverse situation a tight transition state results in the upper left region. If the sum of bond order to nucleophile plus leaving group is unity, the transition state will lie on the synchronicity diagonal.

If the experimental errors are underestimated, it can lead to tight but inaccurate distance bounds. Conversely, the overestimated errors can lead to unnecessarily imprecise distance bounds. RANDMARDI takes into account two types of experimental errors relative integration errors and absolute errors due to spectral noise. The first kind can be estimated, for example, by comparing intensities of symmetric peaks below and above the diagonal, and the second type can be estimated as 50-200% of the lowest quantifiable peak, depending on the spectrum quality. 

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